Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object

Publication date: 7 October 2022

Abstract: We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an irregular, time-dependent rotation under acoustical or optical forces. In this study, we compare reconstruction algorithms in case i) that two-dimensional images of the complex-valued wave are known, or ii) that only the intensity (absolute value) of these images can be measured, which is the case in many practical setups. The latter phase-retrieval problem can be solved by an all-at-once approach based utilizing a hybrid input-output scheme with TV regularization.

Has companion code repository: https://github.com/michaelquellmalz/fourierodt

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Numerical methods for discrete and fast Fourier transforms (65T50) Nonlinear ill-posed problems (47J06) Fourier series and coefficients in several variables (42B05)

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